Contents I Introduction
The GAFEM is a numerical method for solving different problems in engineering and mathematical physics. In the past decades, many researchers were interested in studying the general NS of the boundary value problems (BVPs) and studying, in particular, the NS of the elliptic boundary value problems (EBVP) (and the CLEBVP). There are many different ways to solve the EBVP and CLEBVP we will mention some of them here. In 1978, Ciarlet analysed the basic mathematical aspects of the finite element method within reasonable limits in his book “the finite element method for elliptic problems” [1]. In 1987, Nguyen and White presented the finite-difference procedure for solving a certain type of coupled nonlinear elliptic partial differential equations (CNEPDES) [2]. In 2008, Steinbach introduced in his book “the numerical approximation methods for EBVP”, the main focus of his book was on the numerical analysis of boundary integral equation [3]. In 2014, Jalil and Izadian applied the generalised finite differences method (FDM) for solving the Poisson's equation with Dirichlet boundary conditions (DBCs) [4], also in this year, Quarteroni was described in chapter four of his book the NS of the EBVP by introducing the GAFEM [5]. In 2016, Anley introduced the NS of the EPDE by using the finite volume method [6]. Finally, in 2018, a novel Pandey and Jaboob presented FDM for solving the system of the BVPs of DBCs [7]. All these studies motivated us to study the NS for the CLEBVP using the GAFEM.
